Geodesic
Two spaces homeomorphic to $Seq(p)$
Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 209-218 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider the spaces called $Seq(u_t)$, constructed on the set $Seq$ of all finite sequences of natural numbers using ultrafilters $u_t$ to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that $S(u_t)$ is homogeneous if and only if all the ultrafilters $u_t$ have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to $Seq(p)$ (i.e., $u_t = p$ for all $t\in Seq$). It follows that for a Ramsey ultrafilter $p$, $Seq(p)$ is a topological group.
We consider the spaces called $Seq(u_t)$, constructed on the set $Seq$ of all finite sequences of natural numbers using ultrafilters $u_t$ to define the topology. For such spaces, we discuss continuity, homogeneity, and rigidity. We prove that $S(u_t)$ is homogeneous if and only if all the ultrafilters $u_t$ have the same Rudin-Keisler type. We proved that a space of Louveau, and in certain cases, a space of Sirota, are homeomorphic to $Seq(p)$ (i.e., $u_t = p$ for all $t\in Seq$). It follows that for a Ramsey ultrafilter $p$, $Seq(p)$ is a topological group.
Classification : 54A35, 54C05, 54D80, 54G05, 54H11
Keywords: ultrafilters; continuity; homeomorphisms; homogeneous; rigid; topological group; Ramsey ultrafilters; selective ultrafilters 
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     title = {Two spaces homeomorphic to $Seq(p)$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {209--218},
     year = {2001},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a16/}
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Vaughan, Jerry E. Two spaces homeomorphic to $Seq(p)$. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) no. 1, pp. 209-218. http://geodesic.mathdoc.fr/item/CMUC_2001_42_1_a16/